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udlbook
2023-12-24 10:03:28 -05:00
parent 182293e8d6
commit dbde6d3d89
1 changed files with 40 additions and 14 deletions
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54
Notebooks/Chap05/5_1_Least_Squares_Loss.ipynb
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@@ -4,7 +4,6 @@
"metadata": { "metadata": {
"colab": { "colab": {
"provenance": [], "provenance": [],
"authorship_tag": "ABX9TyOJeBMhN9fXO8UepZ4+Pbg6",
"include_colab_link": true "include_colab_link": true
}, },
"kernelspec": { "kernelspec": {
@@ -433,12 +432,25 @@
"cell_type": "code", "cell_type": "code",
"source": [ "source": [
"# Now let's plot the likelihood, negative log likelihood, and least squares as a function the value of the offset beta1\n", "# Now let's plot the likelihood, negative log likelihood, and least squares as a function the value of the offset beta1\n",
"fig, ax = plt.subplots(1,3)\n", "fig, ax = plt.subplots(1,2)\n",
"fig.set_size_inches(10.5, 3.5)\n", "fig.set_size_inches(10.5, 5.5)\n",
"fig.tight_layout(pad=3.0)\n", "fig.tight_layout(pad=10.0)\n",
"ax[0].plot(beta_1_vals, likelihoods); ax[0].set_xlabel('beta_1[0]$'); ax[0].set_ylabel('likelihood')\n", "likelihood_color = 'tab:red'\n",
"ax[1].plot(beta_1_vals, nlls); ax[1].set_xlabel('beta_1[0]'); ax[1].set_ylabel('negative log likelihood')\n", "nll_color = 'tab:blue'\n",
"ax[2].plot(beta_1_vals, sum_squares); ax[2].set_xlabel('beta_1[0]'); ax[2].set_ylabel('sum of squares')\n", "\n",
"ax[0].set_xlabel('beta_1[0, 0]')\n",
"ax[0].set_ylabel('likelihood', color = likelihood_color)\n",
"ax[0].plot(beta_1_vals, likelihoods, color = likelihood_color)\n",
"ax[0].tick_params(axis='y', labelcolor=likelihood_color)\n",
"\n",
"ax00 = ax[0].twinx()\n",
"ax00.plot(beta_1_vals, nlls, color = nll_color)\n",
"ax00.set_ylabel('negative log likelihood', color = nll_color)\n",
"ax00.tick_params(axis='y', labelcolor = nll_color)\n",
"\n",
"plt.axvline(x = beta_1_vals[np.argmax(likelihoods)], linestyle='dotted')\n",
"\n",
"ax[1].plot(beta_1_vals, sum_squares); ax[1].set_xlabel('beta_1[0]'); ax[1].set_ylabel('sum of squares')\n",
"plt.show()" "plt.show()"
], ],
"metadata": { "metadata": {
@@ -519,12 +531,26 @@
"cell_type": "code", "cell_type": "code",
"source": [ "source": [
"# Now let's plot the likelihood, negative log likelihood, and least squares as a function the value of the standard divation sigma\n", "# Now let's plot the likelihood, negative log likelihood, and least squares as a function the value of the standard divation sigma\n",
"fig, ax = plt.subplots(1,3)\n", "fig, ax = plt.subplots(1,2)\n",
"fig.set_size_inches(10.5, 3.5)\n", "fig.set_size_inches(10.5, 5.5)\n",
"fig.tight_layout(pad=3.0)\n", "fig.tight_layout(pad=10.0)\n",
"ax[0].plot(sigma_vals, likelihoods); ax[0].set_xlabel('$\\sigma$'); ax[0].set_ylabel('likelihood')\n", "likelihood_color = 'tab:red'\n",
"ax[1].plot(sigma_vals, nlls); ax[1].set_xlabel('$\\sigma$'); ax[1].set_ylabel('negative log likelihood')\n", "nll_color = 'tab:blue'\n",
"ax[2].plot(sigma_vals, sum_squares); ax[2].set_xlabel('$\\sigma$'); ax[2].set_ylabel('sum of squares')\n", "\n",
"\n",
"ax[0].set_xlabel('sigma')\n",
"ax[0].set_ylabel('likelihood', color = likelihood_color)\n",
"ax[0].plot(sigma_vals, likelihoods, color = likelihood_color)\n",
"ax[0].tick_params(axis='y', labelcolor=likelihood_color)\n",
"\n",
"ax00 = ax[0].twinx()\n",
"ax00.plot(sigma_vals, nlls, color = nll_color)\n",
"ax00.set_ylabel('negative log likelihood', color = nll_color)\n",
"ax00.tick_params(axis='y', labelcolor = nll_color)\n",
"\n",
"plt.axvline(x = sigma_vals[np.argmax(likelihoods)], linestyle='dotted')\n",
"\n",
"ax[1].plot(sigma_vals, sum_squares); ax[1].set_xlabel('sigma'); ax[1].set_ylabel('sum of squares')\n",
"plt.show()" "plt.show()"
], ],
"metadata": { "metadata": {
@@ -564,4 +590,4 @@
} }
} }
] ]
} }